Conservatives might say it is unfair to tax the rich at a greater percentage than a poor person, that it is only a means to "punish" a person for being "successful".
However, if you think about this, a progressive tax system is perfectly fair:
the decreasing utility value of money
utility is a measure for the degree of happiness or benefit something of value gives you.
It is true that the more you have of something, the less utility value each additional unit carries. This is called "diminishing returns". For example, you like chocolate ice cream, and you enter into an ice cream cone eating contest. After eating one cone, you gain a certain amount of satisfaction. After eating your second, you gain satisfaction, but it is less than the original. Once you've devoured the third, you're starting to get sick of eating ice cream. You barely choke down the fourth, and refuse the fifth because you just don't want to eat any more chocolate ice cream.
This principle is also true with money. The richer you become (the more dollars you have), the less utility value each extra dollar has.
For example, if a person making 30,000 dollars a year gets a 3000 dollar raise, it will mean a significant increase in the person's standard of living (total utility). They might be able to put money down for a new car to replace their old clunker, or take a trip to Hawaii, or move into a better appartement, eat at fancier restaurants. This is a 10% increase in income, but because the person has relatively few dollars, the utility increase is very high.
Now take a person making 3 million dollars a year. Suddenly they get a 300,000 dollar raise (that's 10% of their income, the same as the poor person). The utility difference between 3 million and 3.3 million is not significant. At 3 million dollars, the rich person is probably living in the most luxurious house they desire to, they probably eat at the finest restaurants available already. They most likely have a lot of their income ivested, put to the purpose of making even more money. An extra 300k a year is not going to mean much to their standard of living.
Now, if you tax each person at a rate of 10% (lets assume both their salaries have reverted to the original 30k and 3 mil) the poorer person will bear a higher utility burden from this tax than the rich person, because the poorer person's marginal dollar carries more value than the rich person's. Therefore the flat tax rate of 10% is unfair.
If we want to maximize society's standard of living, we need not to equalize the percentage of income people pay in taxes, but rather to try to equalize the utility burden borne by each income bracket. this means charging the rich a greater percentage of their income, and probably charging the poorer person less of a percentage.